Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ane5)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=5, a₂>=5

For fixed z and a₁=5, a₂=11/2, b₁>=-11/2

For fixed z and a₁=5, a₂=11/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.ane5.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(5/2), -(1/2)}, -z] == (1/42525) (42525 - 935550 z - 24324300 z^2 - 567567000 z^3 + 4605400800 z^4 - 8536207680 z^5 + 6585546240 z^6 - 2596354560 z^7 + 576826560 z^8 - 75644160 z^9 + 5918136 z^10 - 268944 z^11 + 6496 z^12 - 64 z^13) + (1/42525) ((4 Sqrt[Pi] (389188800 z^(7/2) - 1816214400 z^(9/2) + 2750857200 z^(11/2) - 1916913600 z^(13/2) + 713308680 z^(15/2) - 152999280 z^(17/2) + 19619145 z^(19/2) - 1512360 z^(21/2) + 68040 z^(23/2) - 1632 z^(25/2) + 16 z^(27/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]